# KPK Board 10th Class Math Ch 1 Quadratic Equation Short Questions Answers

## KPK Board 10th Class Math Ch 1 Quadratic Equation Short Questions Answers

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Malakand Board 10th classes short questions Answer

Mardan Board 10th classes short questions Answer

Peshawar Board 10th classes short questions Answer

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Dera Ismail Khan Board 10th classes short questions Answer

Kohat Board 10th classes short questions Answer

Bannu Board 10th classes short questions Answer

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Solve 2x4 – 5w2 + 2 = 0

Solution:              2x4 – 5w2 + 2 = 0……………..(i)

Let w2= x ……….(ii)   Then  w4        w2………….  (iii)

Put  (ii) , (iii) , in (i)

2x2 – 5w + 2 = 0

=>           2x2 – 4x – x  + 2 = 0

=>           2x ( x – 2 ) – 1 ( x-2) = 0

=>           ( x-2 ) (2x – 1) = 0

=>           x- 2 = 0                  or            2x  –  1 = 0

=>           x= 2                        or            2x = 1

=>           x = 1/2

Put       x = 2   in  (ii)                => w2  =  2 take square root

=>        w2        =   +2           =>        w = +2

Put       x = ½  in (ii)                         =>          w2 =   ½  take square root

=> w2        =   +½                 =>         w  =  +½   = + 1/2

Solution set  =  {+2 = + 1/2}

Find the constant a and b such that x = -1 and x = 1 are both solutions to the equation

ax2 + bx + 2 = 0

Solution       ax2 + bx + 2 = 0   ……..….(i)

Put  x  = -1  in  (i)                   =>        a(-1)2+ b ( -1 ) + 2 = 0

=>        a – b  +  2  =  0            ………………(iii)

Put   x = 1   in  (i)                     =>        a(1)2+ b (1)+ 2=0

=>        a + b + 2  =  0              (iv)

a – b + 2 = 0

(a+b+2=0)/(2a+4=0)

=>        2a = – 4                        =>        a = – 4/2

=>        2a  = -4                        =>        a =  -4/2

=>        a = -2               put   a = -2   in (iv)

=>        – 2 + b + 2 = 0              =>        b = 0

Thus     a = – 2 ,   b = 0  Ans.

Find all values of x such that x2+ 5x + 6 = 0 and x2+ 19x + 34 = 0 are equal.

Solution:          Since    x2+ 5x+6=0 and x2+ 19x+34 =0  are equal.

Then                x2+ 5x+6 =  x2+ 19x+34

=>        x2+x2+ 5x-19=34- 6=0

=>        – 14 x = 28                   =>        x= -28/14

=>        x = -2   Ans.

Challenge: Find the solution to the equation.

49x^2- 316+123=0

Solution:          49x2– 316+123=0

=>        49x2– 294x-22x+123=0

=>        49x (x-6)-22(x –  6 )=0

=>        (x-6)   (49x -22)=0

=>        (x-6)  =0                       or         49x -22=0

=>        x  = 6                           or         49x = 22

=>        x= 22/49

=>        Thus solution set  =   { 6 , 22/49  }

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